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Find the exact solution to: ln(x) + ln(7) = ln(21)

Log rules: log(a) + log(b) = log(ab) so, in this case, we must find x such that 7x = 21 thus x = 3 similarly, log(a) - log(b) = log(a/b) rearranging the original equation we get: ln(x) = ln(21) - ln(7) so x ...
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Answered by Bryan P. • Maths tutor
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Write sqrt(50) in the form Asqrt(50) where A is an integer

Note that sqrt(ab)=sqrt(a)sqrt(b) Thus to have A, an integer, we must find the highest number 'a' that is a square number and is also a factor of 50. So, a=25 and b=2 (ab=25x2=50) and we have: sqrt(50) = sqr...
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Answered by Bryan P. • Maths tutor
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Prove the identity: sin^2(x)+cos^2(x) = 1

This is one of the most commonly used A level identities which can be proved using only GCSE maths! Firstly, take an arbitrary right angle triangle with Hypotenuse h, and angle x between h and the adjacent s...
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Answered by Sean O. • Maths tutor
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Differentiate the function f(x) = x*sin(x)

This function is the product of the two functions 'x' and 'sin(x)'. Therefore we use the product rule, which says that the differential of a product of two functions is the differential of the first multipli...
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Answered by Dylan B. • Maths tutor
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When and how do I use integration by parts?

Integration by parts is used when you would like to find the integral of a composite function made up of two functions of the same variable as which you're integrating with respect to. The formula for this t...
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Answered by Craig Y. • Maths tutor
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